નિશ્વાયક — ગણિત ધોરણ 12 સાયન્સ — Question

$\frac{R_{21}(1)}{R_{31}(1)} \ \ \ \begin{vmatrix}a+b+c&a+b+c&a+b+c\\2b&b-c-a&2b\\2c&2c&c-a-b\end{vmatrix}$

$=(a+b+c)\begin{vmatrix}1&1&1\\2b&b-c-a&2b\\2c&2c&c-a-b\end{vmatrix}$

$=\xrightarrow[{C\_\{ 13\} ( - 1)}]{{C\_\{ 12\} ( - 1)}} =(a+b+c) \begin{vmatrix}1&0&0\\2b&-(a+b+c)&0\\2c&0&-(c+a+b)\end{vmatrix}$

$ =(a+b+c)^3 \begin{vmatrix}1&0&0\\2b&-(1)&0\\2c&0&-(1)\end{vmatrix}$

$= (a+b+c)^3 (1(1-0))$

$= (a+b+c)^3$